Subject-Specific Predictive Musculoskeletal Simulations of Lower-Limb Exoskeleton Assistance: Metabolic and Biomechanical Effects of Joint Assistance Strategies

Neethan Ratnakumar; Mariya Tohfafarosh; Xianlian Zhou

cs.ROOct 2, 2026

Subject-Specific Predictive Musculoskeletal Simulations of Lower-Limb Exoskeleton Assistance: Metabolic and Biomechanical Effects of Joint Assistance Strategies

Authors: Neethan Ratnakumar, Mariya Tohfafarosh, Xianlian Zhou

Organizations: Department of Mechanical Engineering, University of Jaffna, Sri Lanka · Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, New Jersey, 07102, USA

Abstract

Lower-limb exoskeletons have made considerable progress in reducing energy expenditure during walking. However, designing optimal assistance strategies remains challenging, particularly given inter-individual variability in anthropometry and biomechanics. This study explores energy-optimal lower-limb joint-assistance strategies using predictive simulations with musculoskeletal models. Subject-specific models of six able-bodied subjects, with BMI-based muscle strength scaling, were used in predictive simulations to generate gait at self-selected walking speeds. Ideal actuators were incorporated to simulate various combinations of joint assistance at peak levels of 25 Nm and 50 Nm to examine the effects of assistance on gait and metabolic savings. The effects of each assistance configuration were assessed through cost of transport (COT), joint kinematics, muscle activations, assistive torques, and joint-level power metrics to characterize the biomechanical and energetic impacts of different assistance strategies. At 50 Nm, combined H+K+A (hip-knee-ankle) assistance resulted in the greatest mean COT reduction of 48.50 +/- 4.55%, with individual reductions ranging from 42.22% to 54.65% across the subjects. Among single-joint conditions, assisting the hip was most effective, reducing COT by 31.77 +/- 5.21%; the knee and ankle produced smaller, comparable reductions (19.17% and 17.02%). H+A (hip-ankle) assistance (44.60 +/- 7.08%) emerged as the most effective two-joint assistive configuration. Increasing the torque bound increased positive assistive power primarily at the hip and ankle, while knee assistance showed little sensitivity and delivered positive power near pre-swing. These results support H+A assistance as an efficient two-actuator target, while identifying the knee's atypical pre-swing power strategy as a candidate for targeted experimental validation.

Figures & tables

Figure 1: \par Overview of the OpenSim Moco optimal-control framework used to generate the unassisted and exoskeleton-assisted predictive walking simulations. Exoskeleton assistance is modeled as ideal torque actuation at the joint coordinates, optimized together with other variables such as muscle control and joint angles.

Figure 2: \par The generic and scaled musculoskeletal models. The cross-sectional size of each muscle is scaled proportionally to its maximum isometric force, with floor contact represented by contact spheres.

Subject ID	Age	Height (m)	Weight (kg)	BMI	Sex	Tracking Speed (m/s)
AB06	20	1.80	74.84	23.10	M	1.42
AB07	20	1.65	55.34	20.33	M	0.92
AB14	22	1.52	58.41	25.28	F	1.68
AB15	21	1.78	96.16	30.35	M	1.21
AB18	19	1.80	60.13	18.56	F	1.46
AB24	21	1.73	72.57	24.25	F	1.37

Table 1: \par Subject Demographics and Tracking Data Walking Speeds

Figure 3: \par Hip flexion-extension angles from predictive tracking simulations across seven exoskeleton assistance conditions (

50~\mathrm{Nm\par}

) and the unassisted baseline (NoExo). Each subplot shows the hip angle profile obtained by solving the optimal control problem for the specific condition. The solid purple line and shaded area represent the mean

\pm

standard deviation across subject-specific simulations. For each subject-specific model, one representative unassisted gait cycle from that subject was used as the tracking reference. The dashed tracking mean data are averaged from the six subjects, and the experimental angle data from all subjects in Camargo et al. [ camargo2021comprehensive\par\par ] is shown in black.

Figure 4: \par Knee flexion-extension angles resulting from predictive tracking simulations across seven exoskeleton assistance conditions (

50~\mathrm{Nm\par}

) and the unassisted baseline (NoExo). Each subplot shows the knee angle profile obtained by solving the optimal control problem for the specific condition. The solid purple line and shaded area represent the mean

\pm

Figure 5: \par Ankle dorsiflexion-plantarflexion angles resulting from predictive tracking simulations across seven exoskeleton assistance conditions (

50~\mathrm{Nm\par}

) and the unassisted baseline (NoExo). Each subplot shows the ankle angle profile obtained by solving the optimal control problem for the specific condition. The solid purple line and shaded area represent the mean

\pm

Figure 6: \par Overall simulated hip, knee, and ankle joint angles averaged across all subject-specific models at $50~\mathrm{Nm\par}$ assistance condition. The purple solid colored line represents the mean joint angle trajectory, and the shaded area denotes the standard deviation. Experimental data from Camargo et al. [ camargo2021comprehensive\par\par ] is shown in black with a gray shaded region representing $\pm$ 1 SD.

Figure 7: \par Predicted hip assistive torque ( $50~\mathrm{Nm\par}$ ) profiles across the gait cycle for the four exoskeleton configurations (Hip Only, H+A, H+K, and H+K+A) that incorporate the hip assistance. Dashed colored lines indicate individual subject data, while the purple line (with shaded $\pm$ SD) represents the subject-specific model group average. The black line shows the experimental biological hip joint torque from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded $\pm$ SD) depicts the mean of the NoExo condition for the subject-specific models.

Figure 8: \par Predicted knee assistive torque ( $50~\mathrm{Nm\par}$ ) profiles across the gait cycle for the four exoskeleton configurations (Knee Only, H+K, K+A, and H+K+A) that incorporate the knee assistance. Dashed colored lines indicate individual subject data, while the purple line (with shaded $\pm$ SD) represents the subject-specific model group average. The black line shows the experimental biological knee joint torque from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded $\pm$ SD) depicts the mean of the unassisted condition for the subject-specific model.

Figure 9: \par Predicted ankle assistive torque ( $50~\mathrm{Nm\par}$ ) profiles across the gait cycle for the four exoskeleton configurations (Ankle Only, H+A, K+A, and H+K+A) that incorporate the ankle assistance. Dashed colored lines indicate individual subject data, while the purple line (with shaded $\pm$ SD) represents the subject-specific model group average. The black line shows the experimental biological ankle joint torque from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded $\pm$ SD) depicts the mean of the unassisted condition for the subject-specific model.

Figure 10: \par Overall assistive torques for the hip, knee, and ankle joints ( $50~\mathrm{Nm\par}$ ) obtained across all subjects and exoskeleton assistance conditions. Purple solid lines represent the predicted mean assistive torque profiles across all subjects and conditions, with purple shaded regions denoting $\pm$ 1 standard deviation. The black line shows the experimental biological joint torque from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded $\pm$ SD) depicts the mean of the NoExo (unassisted) condition for the subject-specific model.

Figure 11: \par Predicted hip joint power under

50~\mathrm{Nm\par}

assistance across the gait cycle for the four exoskeleton configurations (Hip Only, H+A, H+K, and H+K+A) that incorporate the hip. Dashed colored lines indicate individual subject data, while the purple line (with shaded

\pm

SD) represents the subject-specific model group average. The black line shows the experimental biological hip joint power profile from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded

\pm

SD) depicts the mean of the NoExo condition for the subject-specific model.

Figure 12: \par Predicted knee joint power under

50~\mathrm{Nm\par}

assistance across the gait cycle for the four exoskeleton configurations (Knee Only, H+K, K+A, and H+K+A) that incorporate the knee. Dashed colored lines indicate individual subject data, while the purple line (with shaded

\pm

SD) represents the subject-specific model group average. The black line shows the experimental biological knee joint power profile from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded

\pm

SD) depicts the mean of the NoExo condition for the subject-specific model.

Figure 13: \par Predicted ankle joint power under

50~\mathrm{Nm\par}

assistance across the gait cycle for the four exoskeleton configurations (Ankle Only, H+A, K+A, and H+K+A) that incorporate the ankle. Dashed colored lines indicate individual subject data, while the purple line (with shaded

\pm

SD) represents the subject-specific model group average. The black line shows the experimental biological ankle joint power profile from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded

\pm

SD) depicts the mean of the NoExo condition for the subject-specific model.

Figure 14: \par Overall assistive power for the hip, knee, and ankle joints ( $50~\mathrm{Nm\par}$ ) obtained across all subjects and exoskeleton assistance conditions. Purple solid lines represent the predicted mean assistive power profiles across all subjects and conditions, with purple shaded regions denoting $\pm$ 1 standard deviation. The black line shows experimental the biological joint power from Camargo et al. [ camargo2021comprehensive\par\par ] , and the green line (with shaded $\pm$ SD) depicts the mean of the NoExo (unassisted) condition for the subject-specific model.

Figure 15: \par Muscle activation profiles across nine lower-limb muscles over the gait cycle, averaged across subjects, under NoExo and seven exoskeleton assistance conditions (Hip Only, Knee Only, Ankle Only, H+K, H+A, K+A, H+K+A) at $50~\mathrm{Nm\par}$ assistive torque. The blue curves in different shades show the single-joint conditions, the red shaded lines show the double-joint conditions, and the purple line shows the three-joint condition. The black line shows experimental biological muscle activations from Camargo et al. [ camargo2021comprehensive\par\par ] (with shaded $\pm$ SD), and the green line depicts the mean of the NoExo condition for the subject-specific models. *Note: The surface EMG data for IL and BFSH were not available in the dataset as they are deep muscles that are difficult to measure. In the GMax panel, the black experimental curve corresponds to GMed, as GMax data were not available.

Joint	Torque (Nm)	Condition	MPP (W/kg)	MNP (W/kg)	PPR	Metabolic Reduction (W/kg)
\multirow 8*Hip	\multirow 4*25	Hip Only	0.279	-0.052	0.843	1.032
		H+A	0.274	-0.053	0.838	1.442
		H+K	0.276	-0.049	0.849	1.345
		H+K+A	0.248	-0.062	0.800	1.778
	\multirow 4*50	Hip Only	0.375	-0.081	0.822	1.323
		H+A	0.371	-0.085	0.814	1.869

Table 2: \par Subjects’ mean power of individual joints under

25~\mathrm{Nm\par}

and

50~\mathrm{Nm\par}

assistive torques and different combinations of joint assistance. The corresponding metabolic reduction is also presented.

Joint	$\tau$ (Nm)	MPP (W/kg)	MNP (W/kg)	PPR	$\tau_{MAX}$ (Nm/kg)	$\tau_{RMS}$ (Nm/kg)
\multirow 2*Hip	25	0.267	-0.052	0.837	0.372	0.246
	50	0.359	-0.079	0.820	0.729	0.394
\multirow 2*Knee	25	0.163	-0.084	0.660	0.310	0.162
	50	0.168	-0.082	0.672	0.339	0.167
\multirow 2*Ankle	25	0.124	-0.032	0.795	0.372	0.181
	50	0.205	-0.033	0.861	0.745	0.283

Table 3: \par Mean Joint Power Magnitudes under 25 Nm and 50 Nm assistive torques (averaged from all corresponding joint assistance cases). All PPR values were computed from the instantaneous joint power time series using Eq. 2.4 \par Power analysis . For comparison, the unassisted biological knee PPR, computed the same way, was 0.352 for the predicted NoExo condition and 0.162 for the experimental data.

Figure 16: \par Mean COT values across exoskeleton assistance configurations at both $25~\mathrm{Nm\par}$ and $50~\mathrm{Nm\par}$ assistance levels. Colored dots represent individual subject-specific model results, with group means and standard deviations shown as bars.The cross-hatched bars are for $25~\mathrm{Nm\par}$ , and the solid-color bars represent the mean COT for $50~\mathrm{Nm\par}$ . The dashed line marks the mean unassisted NoExo COT. The percentage reduction in COT relative to the unassisted NoExo condition is shown above each bar.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Muscle	AB06	AB07	AB14	AB15	AB18	AB24
HAMS	3071	2042	2990	5421	1846	3243
BFSH	914	608	890	1614	550	966
GMAX	2211	1470	2152	3903	1329	2335
IL	2664	1771	2593	4702	1601	2813
RF	1330	884	1294	2347	799	1404
VAS	5687	3781	5536	10038	3419	6006

Appendix

Table 4: \par Maximum isometric muscle forces (N) for the subject-specific models obtained by scaling the generic model values based on subject anthropometry.

Muscle	Max Iso. Force (N)	Opt. Fiber (m)	Slack Length (m)	Pennation (rad)
HAMS	2700	0.1091	0.3262	0.0000
BFSH	804	0.1719	0.0884	0.4014
GMAX	1944	0.1548	0.0723	0.0000
IL	2342	0.0975	0.1560	0.1396
RF	1169	0.1142	0.3104	0.0873
VAS	5000	0.1077	0.1168	0.0524

Appendix

Table 5: \par Key muscle properties for the generic model.

25 Nm
Condition	AB06	AB07	AB14	AB15	AB18	AB24
Hip Only	25.85	27.51	25.72	15.82	30.10	21.62
Knee Only	16.08	17.10	18.13	16.61	20.10	15.18
Ankle Only	12.16	11.19	14.41	8.64	11.51	13.21
H+K	32.88	32.34	33.42	26.16	34.73	26.31
H+A	36.25	35.81	37.35	23.50	38.84	31.94

Appendix

Table 6: \par Percentage reduction in COT relative to the unassisted (NoExo) condition for each subject across assistance configurations at 25, and 50 Nm

Comparison	Test	Statistic	Raw $p$	Holm-adjusted $p$
H, K, A	Exact Friedman	$Q=9.33$	0.0055	0.0166 (significant)
H+K, H+A, K+A	Exact Friedman	$Q=9.00$	0.0081	0.0166 (significant)
H+K+A versus H+A	Exact paired Wilcoxon signed-rank	$W=1.00$	0.0625	0.0625 (not significant)

Appendix

Table 7: \par Statistical comparisons of COT reduction among assistance configurations at

50~\mathrm{Nm\par}

Figure 17: \par Hip flexion-extension angles resulting from predictive tracking simulations across seven exoskeleton assistance conditions (25 Nm) and the unassisted baseline (NoExo). Each subplot shows the hip angle profile obtained by solving the optimal control problem for the specific condition.

Figure 18: \par Knee flexion-extension angles resulting from predictive tracking simulations across seven exoskeleton assistance conditions (25 Nm) and the unassisted baseline (NoExo). Each subplot shows the knee angle profile obtained by solving the optimal control problem for the specific condition.

Figure 19: \par Ankle dorsiflexion-plantarflexion angles resulting from predictive tracking simulations across seven exoskeleton assistance conditions (25 Nm) and the unassisted baseline (NoExo). Each subplot shows the ankle angle profile obtained by solving the optimal control problem for the specific condition.

Figure 20: \par Predicted hip assistive torque (25 Nm) profiles across the gait cycle for the four exoskeleton configurations (Hip Only, H+A, H+K, and H+K+A) that incorporate the hip.

Figure 21: \par Predicted knee assistive torque (25 Nm) profiles across the gait cycle for the four exoskeleton configurations (Knee Only, H+K, K+A, and H+K+A) that incorporate the knee.

Figure 22: \par Predicted ankle assistive torque (25 Nm) profiles across the gait cycle for the four exoskeleton configurations (Ankle Only, H+A, K+A, and H+K+A) that incorporate the ankle.

Figure 23: \par Predicted hip joint power under 25 Nm assistance across the gait cycle for the four exoskeleton configurations (Hip Only, H+A, H+K, and H+K+A) that incorporate the hip.

Figure 24: \par Predicted knee joint power under 25 Nm assistance across the gait cycle for the four exoskeleton configurations (Knee Only, H+K, K+A, and H+K+A) that incorporate the knee.

Figure 25: \par Predicted ankle joint power under 25 Nm assistance across the gait cycle for the four exoskeleton configurations (Ankle Only, H+A, K+A, and H+K+A) that incorporate the ankle.

Figure 26: \par Muscle activation profiles across nine lower-limb muscles over the gait cycle, averaged across subjects, under NoExo and seven exoskeleton assistance conditions (Hip Only, Knee Only, Ankle Only, H+K, H+A, K+A, H+K+A) at $25~\mathrm{Nm\par}$ assistive torque. *Note: The experimental data for iliopsoas and biceps femoris short head was not available.

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Effects of Assistance Delay on Joint Mechanics and Energetics in Biological Torque Control of a Hip Exoskeleton

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Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA

Exoskeleton Torque Agile Locomotion Uncertain Joint Stiffness Assistant Impact Analysis

Open paper AskPDF arXiv

Biological torque control directly maps an estimated human joint moment to exoskeleton assistance, providing a task-agnostic strategy for supporting diverse locomotor activities. However, it remains unclear whether a fixed state-to-torque mapping provides effective assistance across biomechanically distinct tasks. We examined how assistance delay affected hip exoskeleton performance during level-ground (LG), ramp-ascent (RA), and ramp-descent (RD) walking. Eight participants completed a zero-torque baseline condition and five active assistance conditions with delays ranging from 40 to 320 ms. Across tasks and active delays, assistance reduced net metabolic rate by 5.24%, positive biological hip joint work by 5.86%, and total lower-limb positive joint work by 1.68% (all p < 0.05). Assistance delay affected both joint-work outcomes (both p < 0.001) but not net metabolic rate. Mechanical unloading generally decreased with increasing delay, whereas metabolic benefits remained comparatively stable. Relative to the zero-torque condition, net metabolic rate decreased by 9.75% during LG and 7.20% during RA but increased by 1.23% during RD. We did not detect task-dependent differences in the delay response. Our findings indicate that biological torque mappings should be evaluated based on the target outcome and mechanical role of the assisted joint, and that predominantly positive-power assistance may not generalize to negative-work-dominant locomotion without modification.

Abstract

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